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Linear relationships such as y = 2 and y = x all graph out as straight lines. When graphing y = 2, you get a line going horizontally at the 2 mark on the y-axis. When graphing y = x , you get a ...

The graph clearly shows that the slope is continually changing; it isn’t a constant. With a linear relationship, the slope never changes. In this example, one of the fundamental assumptions of simple regression analysis is violated, and you need another approach to estimate the relationship between X and Y.

www.mathsisfun.com/algebra/linear-equations.html

Example: y = 2x + 1 is a linear equation: The graph of y = 2x+1 is a straight line . When x increases, y increases twice as fast, so we need 2x; When x is 0, y is already 1. So +1 is also needed; And so: y = 2x + 1; Here are some example values:

graphpaperdiaries.com/2016/11/30/5-examples-of-linear-relationships-that-are...

The follow up covered a study that rejected a linear model, and instead grouped respondents in to “traditional”, “egalitarian” and “counter-cultural” couples. Despite the claims of the original study, they found that the relationships were only really linear within the groups, but that it was 3 different linear relationships.

www.investopedia.com/terms/l/linearrelationship.asp

For example, you could look at the sale of ice-cream and the number of hospital visits as the two variables at play in a graph and find a linear relationship between the two. Take the Next Step to ...

schools.wikia.org/wiki/Relationships_(Direct,_Linear,_Etc)_Graphs,_Best-Fit_Lines

Linear Relationships in Physics Edit. Linear relationships between velocity and distance show a straight line. In physics, many variables are in linear relationship. Take the equation for velocity, v=d/t, for example, there is a direct relationship between velocity and distance.

sciencing.com/non-linear-relationship-10003107.html

The easiest way to differentiate a linear relationship from a nonlinear relationship is by mapping them on a graph. Use the x-axis of the graph to represent one of the quantities and the y-axis to represent the other. Using the previous example, plot hours worked on the x-axis and money earned on the y-axis.